Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach

Abstract

We present a new large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the distribution of the local density of states (LDoS) down to very small probability tails as small as $10^{-50}$ which are completely out of reach for standard numerical techniques. We perform a thorough analysis of the functional form and of the tails of the probability distribution of the LDoS which yields for the first time a direct, transparent, and precise estimation of the correlation volume close to the Anderson transition. Such correlation volume is found to diverge exponentially when the localization is approached from the delocalized regime, in a singular way that is in agreement with the analytic predictions of the supersymmetric treatment.

11 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1810.07545

References in corpus (18)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization of ultrasound in a three-dimensional elastic network
• Recent progress in many-body localization
• Ergodicity breaking in a model showing many-body localization
• Non-ergodic phases in strongly disordered random regular graphs
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Delocalized Glassy Dynamics and Many Body Localization
• Critical behavior at the localization transition on random regular graphs
• Critical properties of the Anderson localization transition and the high dimensional limit
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Eigenstate correlations around many-body localization transition
• Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees
• Convex Hulls of Random Walks: Large-Deviation Properties
• Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

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